F2C2: a fast tool for the computation of flux coupling in genome-scale metabolic networks

Genome-scale metabolic modeling of the human milk oligosaccharide utilization by Bifidobacterium longum subsp. infantis

Bifidobacterium longum subsp. infantis is a representative and dominant species in the infant gut and is considered a beneficial microbe. This organism displays multiple adaptations to thrive in the infant gut, regarded as a model for human milk oligosaccharides (HMOs) utilization. These carbohydrates are abundant in breast milk and include different molecules based on lactose. They contain fucose, sialic acid, and N-acetylglucosamine. Bifidobacterium metabolism is complex, and a systems view of relevant metabolic pathways and exchange metabolites during HMO consumption is missing. To address this limitation, a refined genome-scale network reconstruction of this bacterium is presented using a previous reconstruction of B. infantis ATCC 15967 as a template. The latter was expanded based on an extensive revision of genome annotations, current literature, and transcriptomic data integration. The metabolic reconstruction (iLR578) accounted for 578 genes, 1,047 reactions, and 924 metabolites. Starting from this reconstruction, we built context-specific genome-scale metabolic models using RNA-seq data from cultures growing in lactose and three HMOs. The models revealed notable differences in HMO metabolism depending on the functional characteristics of the substrates. Particularly, fucosyl-lactose showed a divergent metabolism due to a fucose moiety. High yields of lactate and acetate were predicted under growth rate maximization in all conditions, whereas formate, ethanol, and 1,2-propanediol were substantially lower. Similar results were also obtained under near-optimal growth on each substrate when varying the empirically observed acetate-to-lactate production ratio. Model predictions displayed reasonable agreement between central carbon metabolism fluxes and expression data across all conditions. Flux coupling analysis revealed additional connections between succinate exchange and arginine and sulfate metabolism and a strong coupling between central carbon reactions and adenine metabolism. More importantly, specific networks of coupled reactions under each carbon source were derived and analyzed. Overall, the presented network reconstruction constitutes a valuable platform for probing the metabolism of this prominent infant gut bifidobacteria.IMPORTANCEThis work presents a detailed reconstruction of the metabolism of Bifidobacterium longum subsp. infantis, a prominent member of the infant gut microbiome, providing a systems view of its metabolism of human milk oligosaccharides.

Control Theory and Systems Biology: Potential Applications in Neurodegeneration and Search for Therapeutic Targets

Control theory, a well-established discipline in engineering and mathematics, has found novel applications in systems biology. This interdisciplinary approach leverages the principles of feedback control and regulation to gain insights into the complex dynamics of cellular and molecular networks underlying chronic diseases, including neurodegeneration. By modeling and analyzing these intricate systems, control theory provides a framework to understand the pathophysiology and identify potential therapeutic targets. Therefore, this review examines the most widely used control methods in conjunction with genomic-scale metabolic models in the steady state of the multi-omics type. According to our research, this approach involves integrating experimental data, mathematical modeling, and computational analyses to simulate and control complex biological systems. In this review, we find that the most significant application of this methodology is associated with cancer, leaving a lack of knowledge in neurodegenerative models. However, this methodology, mainly associated with the Minimal Dominant Set (MDS), has provided a starting point for identifying therapeutic targets for drug development and personalized treatment strategies, paving the way for more effective therapies.

On the representativeness and stability of a set of EFMs

MOTIVATION

Elementary flux modes are a well-known tool for analyzing metabolic networks. The whole set of elementary flux modes (EFMs) cannot be computed in most genome-scale networks due to their large cardinality. Therefore, different methods have been proposed to compute a smaller subset of EFMs that can be used for studying the structure of the network. These latter methods pose the problem of studying the representativeness of the calculated subset. In this article, we present a methodology to tackle this problem.

RESULTS

We have introduced the concept of stability for a particular network parameter and its relation to the representativeness of the EFM extraction method studied. We have also defined several metrics to study and compare the EFM biases. We have applied these techniques to compare the relative behavior of previously proposed methods in two case studies. Furthermore, we have presented a new method for the EFM computation (PiEFM), which is more stable (less biased) than previous ones, has suitable representativeness measures, and exhibits better variability in the extracted EFMs.

AVAILABILITY AND IMPLEMENTATION

Software and additional material are freely available at https://github.com/biogacop/PiEFM.

Relative flux trade-offs and optimization of metabolic network functionalities

Trade-offs between traits are present across different levels of biological systems and ultimately reflect constraints imposed by physicochemical laws and the structure of underlying biochemical networks. Yet, mechanistic explanation of how trade-offs between molecular traits arise and how they relate to optimization of fitness-related traits remains elusive. Here, we introduce the concept of relative flux trade-offs and propose a constraint-based approach, termed FluTOr, to identify metabolic reactions whose fluxes are in relative trade-off with respect to an optimized fitness-related cellular task, like growth. We then employed FluTOr to identify relative flux trade-offs in the genome-scale metabolic networks of Escherichia coli, Saccharomyces cerevisiae, and Arabidopsis thaliana. For the metabolic models of E. coli and S. cerevisiae we showed that: (i) the identified relative flux trade-offs depend on the carbon source used and that (ii) reactions that participated in relative trade-offs in both species were implicated in cofactor biosynthesis. In contrast to the two microorganisms, the relative flux trade-offs for the metabolic model of A. thaliana did not depend on the available nitrogen sources, reflecting the differences in the underlying metabolic network as well as the considered environments. Lastly, the established connection between relative flux trade-offs allowed us to identify overexpression targets that can be used to optimize fitness-related traits. Altogether, our computational approach and findings demonstrate how relative flux trade-offs can shape optimization of metabolic tasks, important in biotechnological applications.

Systematizing the different notions of growth-coupled product synthesis and a single framework for computing corresponding strain designs

A widely used design principle for metabolic engineering of microorganisms aims to introduce interventions that enforce growth-coupled product synthesis such that the product of interest becomes a (mandatory) by-product of growth. However, different variants and partially contradicting notions of growth-coupled production (GCP) exist. Herein, we propose an ontology for the different degrees of GCP and clarify their relationships. Ordered by coupling degree, we distinguish four major classes: potentially, weakly, and directionally growth-coupled production (pGCP, wGCP, dGCP) as well as substrate-uptake coupled production (SUCP). We then extend the framework of Minimal Cut Sets (MCS), previously used to compute dGCP and SUCP strain designs, to allow inclusion of implicit optimality constraints, a feature required to compute pGCP and wGCP designs. This extension closes the gap between MCS-based and bilevel-based strain design approaches and enables computation (and comparison) of designs for all GCP classes within a single framework. By computing GCP strain designs for a range of products, we illustrate the hierarchical relationships between the different coupling degrees. We find that feasibility of coupling is not affected by the chosen GCP degree and that strongest coupling (SUCP) requires often only one or two more interventions than wGCP and dGCP. Finally, we show that the principle of coupling can be generalized to couple product synthesis with other cellular functions than growth, for example, with net ATP formation. This work provides important theoretical results and algorithmic developments and a unified terminology for computational strain design based on GCP.

Prospecting Biochemical Pathways to Implement Microbe-Based Production of the New-to-Nature Platform Chemical Levulinic Acid

Levulinic acid is a versatile platform molecule with potential to be used as an intermediate in the synthesis of many value-added products used across different industries, from cosmetics to fuels. Thus far, microbial biosynthetic pathways having levulinic acid as a product or an intermediate are not known, which restrains the development and optimization of a microbe-based process envisaging the sustainable bioproduction of this chemical. One of the doors opened by synthetic biology in the design of microbial systems is the implementation of new-to-nature pathways, that is, the assembly of combinations of enzymes not observed in vivo, where the enzymes can use not only their native substrates but also non-native ones, creating synthetic steps that enable the production of novel compounds. Resorting to a combined approach involving complementary computational tools and extensive manual curation, in this work, we provide a thorough prospect of candidate biosynthetic pathways that can be assembled for the production of levulinic acid in Escherichia coli or Saccharomyces cerevisiae. Out of the hundreds of combinations screened, five pathways were selected as best candidates on the basis of the availability of substrates and of candidate enzymes to catalyze the synthetic steps (that is, those steps that involve conversions not previously described). Genome-scale metabolic modeling was used to assess the performance of these pathways in the two selected hosts and to anticipate possible bottlenecks. Not only does the herein described approach offer a platform for the future implementation of the microbial production of levulinic acid but also it provides an organized research strategy that can be used as a framework for the implementation of other new-to-nature biosynthetic pathways for the production of value-added chemicals, thus fostering the emerging field of synthetic industrial microbiotechnology.

Essential gene prediction using limited gene essentiality information-An integrative semi-supervised machine learning strategy

Essential gene prediction helps to find minimal genes indispensable for the survival of any organism. Machine learning (ML) algorithms have been useful for the prediction of gene essentiality. However, currently available ML pipelines perform poorly for organisms with limited experimental data. The objective is the development of a new ML pipeline to help in the annotation of essential genes of less explored disease-causing organisms for which minimal experimental data is available. The proposed strategy combines unsupervised feature selection technique, dimension reduction using the Kamada-Kawai algorithm, and semi-supervised ML algorithm employing Laplacian Support Vector Machine (LapSVM) for prediction of essential and non-essential genes from genome-scale metabolic networks using very limited labeled dataset. A novel scoring technique, Semi-Supervised Model Selection Score, equivalent to area under the ROC curve (auROC), has been proposed for the selection of the best model when supervised performance metrics calculation is difficult due to lack of data. The unsupervised feature selection followed by dimension reduction helped to observe a distinct circular pattern in the clustering of essential and non-essential genes. LapSVM then created a curve that dissected this circle for the classification and prediction of essential genes with high accuracy (auROC > 0.85) even with 1% labeled data for model training. After successful validation of this ML pipeline on both Eukaryotes and Prokaryotes that show high accuracy even when the labeled dataset is very limited, this strategy is used for the prediction of essential genes of organisms with inadequate experimentally known data, such as Leishmania sp. Using a graph-based semi-supervised machine learning scheme, a novel integrative approach has been proposed for essential gene prediction that shows universality in application to both Prokaryotes and Eukaryotes with limited labeled data. The essential genes predicted using the pipeline provide an important lead for the prediction of gene essentiality and identification of novel therapeutic targets for antibiotic and vaccine development against disease-causing parasites.

Flux Coupling and the Objective Functions' Length in EFMs

Structural analysis of constraint-based metabolic network models attempts to find the network's properties by searching for subsets of suitable modes or Elementary Flux Modes (EFMs). One useful approach is based on Linear Program (LP) techniques, which introduce an objective function to convert the stoichiometric and thermodynamic constraints into a linear program (LP), using additional constraints to generate different nontrivial modes. This work introduces FLFS-FC (Fixed Length Function Sampling with Flux Coupling), a new approach to increase the efficiency of generation of large sets of different EFMs for the network. FLFS-FC is based on the importance of the length of the objective functions used in the associated LP problem and the imposition of additional negative constraints. Our proposal overrides some of the known drawbacks associated with the EFM extraction, such as the appearance of unfeasible problems or multiple repeated solutions arising from different LP problems.

A mechanism-aware and multiomic machine-learning pipeline characterizes yeast cell growth

Metabolic modeling and machine learning are key components in the emerging next generation of systems and synthetic biology tools, targeting the genotype-phenotype-environment relationship. Rather than being used in isolation, it is becoming clear that their value is maximized when they are combined. However, the potential of integrating these two frameworks for omic data augmentation and integration is largely unexplored. We propose, rigorously assess, and compare machine-learning-based data integration techniques, combining gene expression profiles with computationally generated metabolic flux data to predict yeast cell growth. To this end, we create strain-specific metabolic models for 1,143 Saccharomyces cerevisiae mutants and we test 27 machine-learning methods, incorporating state-of-the-art feature selection and multiview learning approaches. We propose a multiview neural network using fluxomic and transcriptomic data, showing that the former increases the predictive accuracy of the latter and reveals functional patterns that are not directly deducible from gene expression alone. We test the proposed neural network on a further 86 strains generated in a different experiment, therefore verifying its robustness to an additional independent dataset. Finally, we show that introducing mechanistic flux features improves the predictions also for knockout strains whose genes were not modeled in the metabolic reconstruction. Our results thus demonstrate that fusing experimental cues with in silico models, based on known biochemistry, can contribute with disjoint information toward biologically informed and interpretable machine learning. Overall, this study provides tools for understanding and manipulating complex phenotypes, increasing both the prediction accuracy and the extent of discernible mechanistic biological insights.

Flux-based hierarchical organization of Escherichia coli's metabolic network

Biological networks across scales exhibit hierarchical organization that may constrain network function. Yet, understanding how these hierarchies arise due to the operational constraint of the networks and whether they impose limits to molecular phenotypes remains elusive. Here we show that metabolic networks include a hierarchy of reactions based on a natural flux ordering that holds for every steady state. We find that the hierarchy of reactions is reflected in experimental measurements of transcript, protein and flux levels of Escherichia coli under various growth conditions as well as in the catalytic rate constants of the corresponding enzymes. Our findings point at resource partitioning and a fine-tuning of enzyme levels in E. coli to respect the constraints imposed by the network structure at steady state. Since reactions in upper layers of the hierarchy impose an upper bound on the flux of the reactions downstream, the hierarchical organization of metabolism due to the flux ordering has direct applications in metabolic engineering.

SWIFTCORE: a tool for the context-specific reconstruction of genome-scale metabolic networks

BACKGROUND

High-throughput omics technologies have enabled the comprehensive reconstructions of genome-scale metabolic networks for many organisms. However, only a subset of reactions is active in each cell which differs from tissue to tissue or from patient to patient. Reconstructing a subnetwork of the generic metabolic network from a provided set of context-specific active reactions is a demanding computational task.

RESULTS

We propose SWIFTCC and SWIFTCORE as effective methods for flux consistency checking and the context-specific reconstruction of genome-scale metabolic networks which consistently outperform the previous approaches.

CONCLUSIONS

We have derived an approximate greedy algorithm which efficiently scales to increasingly large metabolic networks. SWIFTCORE is freely available for non-commercial use in the GitHub repository at https://mtefagh.github.io/swiftcore/.

Network reduction methods for genome-scale metabolic models

Genome-scale metabolic models (GSMs) provide a comprehensive representation of cellular metabolism. GSMs provide a mechanistic link between cellular genotypes and metabolic phenotypes, and are thus widely used to analyze metabolism at the systems level. GSMs consist of hundreds or thousands of reactions. They have thus largely been analyzed with computationally efficient constraint-based methods such as flux-balance analysis, limiting their scope and phenotype prediction accuracy. Computationally more demanding but potentially more informative methods, such as kinetic and dynamic modeling, are currently limited to small or medium-sized models. Thus, it is desirable to achieve unbiased stoichiometric reductions of large-scale metabolic models to small, coarse-grained model representations that capture significant metabolic modules. Here, we review published automated and semiautomated methods used for large-scale metabolic model reduction. The top-down methods discussed provide minimal networks that retain a set of user-protected phenotypes, but may reduce the model's metabolic and phenotypic versatility. In contrast, the two bottom-up approaches reviewed retain a more unbiased set of phenotypes; at the same time, these methods require the partitioning of the GSM into metabolic subsystems by the user, and make strong assumptions on the subsystems' connections and their states, respectively.

Simulation of heterosis in a genome-scale metabolic network provides mechanistic explanations for increased biomass production rates in hybrid plants

Heterosis, or hybrid vigour, is said to occur when F1 individuals exhibit increased performance for a number of traits compared to their parental lines. Improved traits can include increased size, better yield, faster development and a higher tolerance to pathogens or adverse conditions. The molecular basis for the phenomenon remains disputed, despite many decades of theorising and experimentation. In this study, we add a genetics layer to a constraint-based model of plant (Arabidopsis) primary metabolism and show that we can realistically reproduce and quantify heterosis in a highly complex trait (the rate of biomass production). The results demonstrate that additive effects coupled to the complex patterns of epistasis generated by a large metabolic network are sufficient to explain most or all the heterosis seen in typical F1 hybrids. Such models provide a simple approach to exploring and understanding heterosis and should assist in designing breeding strategies to exploit this phenomenon in the future.

Metabolic Model of the Phytophthora infestans-Tomato Interaction Reveals Metabolic Switches during Host Colonization

The oomycete pathogen Phytophthora infestans causes potato and tomato late blight, a disease that is a serious threat to agriculture. P. infestans is a hemibiotrophic pathogen, and during infection, it scavenges nutrients from living host cells for its own proliferation. To date, the nutrient flux from host to pathogen during infection has hardly been studied, and the interlinked metabolisms of the pathogen and host remain poorly understood. Here, we reconstructed an integrated metabolic model of P. infestans and tomato (Solanum lycopersicum) by integrating two previously published models for both species. We used this integrated model to simulate metabolic fluxes from host to pathogen and explored the topology of the model to study the dependencies of the metabolism of P. infestans on that of tomato. This showed, for example, that P. infestans, a thiamine auxotroph, depends on certain metabolic reactions of the tomato thiamine biosynthesis. We also exploited dual-transcriptome data of a time course of a full late blight infection cycle on tomato leaves and integrated the expression of metabolic enzymes in the model. This revealed profound changes in pathogen-host metabolism during infection. As infection progresses, P. infestans performs less de novo synthesis of metabolites and scavenges more metabolites from tomato. This integrated metabolic model for the P. infestans-tomato interaction provides a framework to integrate data and generate hypotheses about in planta nutrition of P. infestans throughout its infection cycle.IMPORTANCE Late blight disease caused by the oomycete pathogen Phytophthora infestans leads to extensive yield losses in tomato and potato cultivation worldwide. To effectively control this pathogen, a thorough understanding of the mechanisms shaping the interaction with its hosts is paramount. While considerable work has focused on exploring host defense mechanisms and identifying P. infestans proteins contributing to virulence and pathogenicity, the nutritional strategies of the pathogen are mostly unresolved. Genome-scale metabolic models (GEMs) can be used to simulate metabolic fluxes and help in unravelling the complex nature of metabolism. We integrated a GEM of tomato with a GEM of P. infestans to simulate the metabolic fluxes that occur during infection. This yields insights into the nutrients that P. infestans obtains during different phases of the infection cycle and helps in generating hypotheses about nutrition in planta.

Evolutionary design principles in metabolism

Microorganisms are ubiquitous and adapt to various dynamic environments to sustain growth. These adaptations accumulate, generating new traits forming the basis of evolution. Organisms adapt at various levels, such as gene regulation, signalling, protein-protein interactions and metabolism. Of these, metabolism forms the integral core of an organism for maintaining the growth and function of a cell. Therefore, studying adaptations in metabolic networks is crucial to understand the emergence of novel metabolic capabilities. Metabolic networks, composed of enzyme-catalysed reactions, exhibit certain repeating paradigms or design principles that arise out of different selection pressures. In this review, we discuss the design principles that are known to exist in metabolic networks, such as functional redundancy, modularity, flux coupling and exaptations. We elaborate on the studies that have helped gain insights highlighting the interplay of these design principles and adaptation. Further, we discuss how evolution plays a role in exploiting such paradigms to enhance the robustness of organisms. Looking forward, we predict that with the availability of ever-increasing numbers of bacterial, archaeal and eukaryotic genomic sequences, novel design principles will be identified, expanding our understanding of these paradigms shaped by varied evolutionary processes.

Designing Metabolic Division of Labor in Microbial Communities

Microbes face a trade-off between being metabolically independent and relying on neighboring organisms for the supply of some essential metabolites. This balance of conflicting strategies affects microbial community structure and dynamics, with important implications for microbiome research and synthetic ecology. A "gedanken" (thought) experiment to investigate this trade-off would involve monitoring the rise of mutual dependence as the number of metabolic reactions allowed in an organism is increasingly constrained. The expectation is that below a certain number of reactions, no individual organism would be able to grow in isolation and cross-feeding partnerships and division of labor would emerge. We implemented this idealized experiment using in silico genome-scale models. In particular, we used mixed-integer linear programming to identify trade-off solutions in communities of Escherichia coli strains. The strategies that we found revealed a large space of opportunities in nuanced and nonintuitive metabolic division of labor, including, for example, splitting the tricarboxylic acid (TCA) cycle into two separate halves. The systematic computation of possible solutions in division of labor for 1-, 2-, and 3-strain consortia resulted in a rich and complex landscape. This landscape displayed a nonlinear boundary, indicating that the loss of an intracellular reaction was not necessarily compensated for by a single imported metabolite. Different regions in this landscape were associated with specific solutions and patterns of exchanged metabolites. Our approach also predicts the existence of regions in this landscape where independent bacteria are viable but are outcompeted by cross-feeding pairs, providing a possible incentive for the rise of division of labor. IMPORTANCE Understanding how microbes assemble into communities is a fundamental open issue in biology, relevant to human health, metabolic engineering, and environmental sustainability. A possible mechanism for interactions of microbes is through cross-feeding, i.e., the exchange of small molecules. These metabolic exchanges may allow different microbes to specialize in distinct tasks and evolve division of labor. To systematically explore the space of possible strategies for division of labor, we applied advanced optimization algorithms to computational models of cellular metabolism. Specifically, we searched for communities able to survive under constraints (such as a limited number of reactions) that would not be sustainable by individual species. We found that predicted consortia partition metabolic pathways in ways that would be difficult to identify manually, possibly providing a competitive advantage over individual organisms. In addition to helping understand diversity in natural microbial communities, our approach could assist in the design of synthetic consortia.

Cellular determinants of metabolite concentration ranges

Cellular functions are shaped by reaction networks whose dynamics are determined by the concentrations of underlying components. However, cellular mechanisms ensuring that a component’s concentration resides in a given range remain elusive. We present network properties which suffice to identify components whose concentration ranges can be efficiently computed in mass-action metabolic networks. We show that the derived ranges are in excellent agreement with simulations from a detailed kinetic metabolic model of Escherichia coli. We demonstrate that the approach can be used with genome-scale metabolic models to arrive at predictions concordant with measurements from Escherichia coli under different growth scenarios. By application to 14 genome-scale metabolic models from diverse species, our approach specifies the cellular determinants of concentration ranges that can be effectively employed to make predictions for a variety of biotechnological and medical applications.

We present a computational approach for inferring concentration ranges from genome-scale metabolic models. The approach specifies a determinant and molecular mechanism underling facile control of concentration ranges for components in large-scale cellular networks. Most importantly, the predictions about concentration ranges do not require knowledge of kinetic parameters (which are difficult to specify at a genome scale), provided measurements of concentrations in a reference state. The approach assumes that reaction rates follow the mass action law used in the derivations of other types of kinetics. We apply the approach with large-scale kinetic and stoichiometric metabolic models of organisms from different kingdoms of life to show that we can identify a proportion of metabolites to which our approach is applicable. By challenging the predictions of concentration ranges in the genome-scale metabolic network of E. coli with real-world data sets, we further demonstrate the prediction power and limitations of the approach.

Quantitative flux coupling analysis

Flux coupling analysis (FCA) aims to describe the functional dependencies among reactions in a metabolic network. Currently studied coupling relations are qualitative in the sense that they identify pairs of reactions for which the activity of one reaction necessitates the activity of the other one, but without giving any numerical bounds relating the possible activity rates. The potential applications of FCA are heavily investigated, however apart from some trivial cases there is no clue of what bottleneck in the metabolic network causes each dependency. In this article, we introduce a quantitative approach to the same flux coupling problem named quantitative flux coupling analysis (QFCA). It generalizes the current concepts as we show that all the qualitative information provided by FCA is readily available in the quantitative flux coupling equations of QFCA, without the need for any additional analysis. Moreover, we design a simple algorithm to efficiently identify these flux coupling equations which scales up to the genome-scale metabolic networks with thousands of reactions and metabolites in an effective way. Furthermore, this framework enables us to quantify the "strength" of the flux coupling relations. We also provide different biologically meaningful interpretations, including one which gives an intuitive certificate of precisely which metabolites in the network enforce each flux coupling relation. Eventually, we conclude by suggesting the probable application of QFCA to the metabolic gap-filling problem, which we only begin to address here and is left for future research to further investigate.

Improving the EFMs quality by augmenting their representativeness in LP methods

Background

Although cellular metabolism has been widely studied, its fully comprehension is still a challenge. A main tool for this study is the analysis of meaningful pieces of knowledge called modes and, in particular, specially interesting classes of modes such as pathways and Elementary Flux Modes (EFMs). Its study often has to deal with issues such as the appearance of infeasibilities or the difficulty of finding representative enough sets of modes that are free of repetitions. Mode extraction methods usually incorporate strategies devoted to mitigate this phenomena but they still get a high ratio of repetitions in the set of solutions.

Results

This paper presents a proposal to improve the representativeness of the full set of metabolic reactions in the set of computed modes by penalizing the eventual high frequency of occurrence of some reactions during the extraction. This strategy can be applied to any linear programming based extraction existent method.

Conclusions

Our strategy enhances the quality of a set of extracted EFMs favouring the presence of every reaction in it and improving the efficiency by mitigating the occurrence of repeated solutions. The new proposed strategy can complement other EFMs extraction methods based on linear programming. The obtained solutions are more likely to be diverse using less computing effort and improving the efficiency of the extraction.

Analysis of Piscirickettsia salmonis Metabolism Using Genome-Scale Reconstruction, Modeling, and Testing

Piscirickettsia salmonis is an intracellular bacterial fish pathogen that causes piscirickettsiosis, a disease with highly adverse impact in the Chilean salmon farming industry. The development of effective treatment and control methods for piscireckttsiosis is still a challenge. To meet it the number of studies on P. salmonis has grown in the last couple of years but many aspects of the pathogen's biology are still poorly understood. Studies on its metabolism are scarce and only recently a metabolic model for reference strain LF-89 was developed. We present a new genome-scale model for P. salmonis LF-89 with more than twice as many genes as in the previous model and incorporating specific elements of the fish pathogen metabolism. Comparative analysis with models of different bacterial pathogens revealed a lower flexibility in P. salmonis metabolic network. Through constraint-based analysis, we determined essential metabolites required for its growth and showed that it can benefit from different carbon sources tested experimentally in new defined media. We also built an additional model for strain A1-15972, and together with an analysis of P. salmonis pangenome, we identified metabolic features that differentiate two main species clades. Both models constitute a knowledge-base for P. salmonis metabolism and can be used to guide the efficient culture of the pathogen and the identification of specific drug targets.

Quantitative time-course metabolomics in human red blood cells reveal the temperature dependence of human metabolic networks

The temperature dependence of biological processes has been studied at the levels of individual biochemical reactions and organism physiology (e.g. basal metabolic rates) but has not been examined at the metabolic network level. Here, we used a systems biology approach to characterize the temperature dependence of the human red blood cell (RBC) metabolic network between 4 and 37 °C through absolutely quantified exo- and endometabolomics data. We used an Arrhenius-type model (Q₁₀) to describe how the rate of a biochemical process changes with every 10 °C change in temperature. Multivariate statistical analysis of the metabolomics data revealed that the same metabolic network-level trends previously reported for RBCs at 4 °C were conserved but accelerated with increasing temperature. We calculated a median Q₁₀ coefficient of 2.89 ± 1.03, within the expected range of 2-3 for biological processes, for 48 individual metabolite concentrations. We then integrated these metabolomics measurements into a cell-scale metabolic model to study pathway usage, calculating a median Q₁₀ coefficient of 2.73 ± 0.75 for 35 reaction fluxes. The relative fluxes through glycolysis and nucleotide metabolism pathways were consistent across the studied temperature range despite the non-uniform distributions of Q₁₀ coefficients of individual metabolites and reaction fluxes. Together, these results indicate that the rate of change of network-level responses to temperature differences in RBC metabolism is consistent between 4 and 37 °C. More broadly, we provide a baseline characterization of a biochemical network given no transcriptional or translational regulation that can be used to explore the temperature dependence of metabolism.

Revealing the mystery of metabolic adaptations using a genome scale model of Leishmania infantum

Human macrophage phagolysosome and sandfly midgut provide antagonistic ecological niches for Leishmania parasites to survive and proliferate. Parasites optimize their metabolism to utilize the available inadequate resources by adapting to those environments. Lately, a number of metabolomics studies have revived the interest to understand metabolic strategies utilized by the Leishmania parasite for optimal survival within its hosts. For the first time, we propose a reconstructed genome-scale metabolic model for Leishmania infantum JPCM5, the analyses of which not only captures observations reported by metabolomics studies in other Leishmania species but also divulges novel features of the L. infantum metabolome. Our results indicate that Leishmania metabolism is organized in such a way that the parasite can select appropriate alternatives to compensate for limited external substrates. A dynamic non-essential amino acid motif exists within the network that promotes a restricted redistribution of resources to yield required essential metabolites. Further, subcellular compartments regulate this metabolic re-routing by reinforcing the physiological coupling of specific reactions. This unique metabolic organization is robust against accidental errors and provides a wide array of choices for the parasite to achieve optimal survival.

Reconstruction of the microalga Nannochloropsis salina genome-scale metabolic model with applications to lipid production

Background

Nannochloropsis salina (= Eustigmatophyceae) is a marine microalga which has become a biotechnological target because of its high capacity to produce polyunsaturated fatty acids and triacylglycerols. It has been used as a source of biofuel, pigments and food supplements, like Omega 3. Only some Nannochloropsis species have been sequenced, but none of them benefit from a genome-scale metabolic model (GSMM), able to predict its metabolic capabilities.

Results

We present iNS934, the first GSMM for N. salina, including 2345 reactions, 934 genes and an exhaustive description of lipid and nitrogen metabolism. iNS934 has a 90% of accuracy when making simple growth/no-growth predictions and has a 15% error rate in predicting growth rates in different experimental conditions. Moreover, iNS934 allowed us to propose 82 different knockout strategies for strain optimization of triacylglycerols.

Conclusions

iNS934 provides a powerful tool for metabolic improvement, allowing predictions and simulations of N. salina metabolism under different media and genetic conditions. It also provides a systemic view of N. salina metabolism, potentially guiding research and providing context to -omics data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0441-1) contains supplementary material, which is available to authorized users.

Discovering missing reactions of metabolic networks by using gene co-expression data

Flux coupling analysis is a computational method which is able to explain co-expression of metabolic genes by analyzing the topological structure of a metabolic network. It has been suggested that if genes in two seemingly fully-coupled reactions are not highly co-expressed, then these two reactions are not fully coupled in reality, and hence, there is a gap or missing reaction in the network. Here, we present GAUGE as a novel approach for gap filling of metabolic networks, which is a two-step algorithm based on a mixed integer linear programming formulation. In GAUGE, the discrepancies between experimental co-expression data and predicted flux coupling relations is minimized by adding a minimum number of reactions to the network. We show that GAUGE is able to predict missing reactions of E. coli metabolism that are not detectable by other popular gap filling approaches. We propose that our algorithm may be used as a complementary strategy for the gap filling problem of metabolic networks. Since GAUGE relies only on gene expression data, it can be potentially useful for exploring missing reactions in the metabolism of non-model organisms, which are often poorly characterized, cannot grow in the laboratory, and lack genetic tools for generating knockouts.

A mixed-integer linear programming approach to the reduction of genome-scale metabolic networks

Background

Constraint-based analysis has become a widely used method to study metabolic networks. While some of the associated algorithms can be applied to genome-scale network reconstructions with several thousands of reactions, others are limited to small or medium-sized models. In 2015, Erdrich et al. introduced a method called NetworkReducer, which reduces large metabolic networks to smaller subnetworks, while preserving a set of biological requirements that can be specified by the user. Already in 2001, Burgard et al. developed a mixed-integer linear programming (MILP) approach for computing minimal reaction sets under a given growth requirement.

Results

Here we present an MILP approach for computing minimum subnetworks with the given properties. The minimality (with respect to the number of active reactions) is not guaranteed by NetworkReducer, while the method by Burgard et al. does not allow specifying the different biological requirements. Our procedure is about 5-10 times faster than NetworkReducer and can enumerate all minimum subnetworks in case there exist several ones. This allows identifying common reactions that are present in all subnetworks, and reactions appearing in alternative pathways.

Conclusions

Applying complex analysis methods to genome-scale metabolic networks is often not possible in practice. Thus it may become necessary to reduce the size of the network while keeping important functionalities. We propose a MILP solution to this problem. Compared to previous work, our approach is more efficient and allows computing not only one, but even all minimum subnetworks satisfying the required properties.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-016-1412-z) contains supplementary material, which is available to authorized users.

An integrative machine learning strategy for improved prediction of essential genes in Escherichia coli metabolism using flux-coupled features

We propose an integrated machine learning process to predict gene essentiality in Escherichia coli K-12 MG1655 metabolism that outperforms known methods.

In silico design of anaerobic growth-coupled product formation in Escherichia coli: experimental validation using a simple polyol, glycerol

Integrated approaches using in silico model-based design and advanced genetic tools have enabled efficient production of fuels, chemicals and functional ingredients using microbial cell factories. In this study, using a recently developed genome-scale metabolic model for Escherichia coli iJO1366, a mutant strain has been designed in silico for the anaerobic growth-coupled production of a simple polyol, glycerol. Computational complexity was significantly reduced by systematically reducing the target reactions used for knockout simulations. One promising penta knockout E. coli mutant (E. coli ΔadhE ΔldhA ΔfrdC ΔtpiA ΔmgsA) was selected from simulation study and was constructed experimentally by sequentially deleting five genes. The penta mutant E. coli bearing the Saccharomyces cerevisiae glycerol production pathway was able to grow anaerobically and produce glycerol as the major metabolite with up to 90% of theoretical yield along with stoichiometric quantities of acetate and formate. Using the penta mutant E. coli strain we have demonstrated that the ATP formation from the acetate pathway was essential for growth under anaerobic conditions. The general workflow developed can be easily applied to anaerobic production of other platform chemicals using E. coli as the cell factory.

Control of fluxes in metabolic networks

Understanding the control of large-scale metabolic networks is central to biology and medicine. However, existing approaches either require specifying a cellular objective or can only be used for small networks. We introduce new coupling types describing the relations between reaction activities, and develop an efficient computational framework, which does not require any cellular objective for systematic studies of large-scale metabolism. We identify the driver reactions facilitating control of 23 metabolic networks from all kingdoms of life. We find that unicellular organisms require a smaller degree of control than multicellular organisms. Driver reactions are under complex cellular regulation in Escherichia coli, indicating their preeminent role in facilitating cellular control. In human cancer cells, driver reactions play pivotal roles in malignancy and represent potential therapeutic targets. The developed framework helps us gain insights into regulatory principles of diseases and facilitates design of engineering strategies at the interface of gene regulation, signaling, and metabolism.

Metabolic Network Constrains Gene Regulation of C4 Photosynthesis: The Case of Maize

Engineering C3 plants to increase their efficiency of carbon fixation as well as of nitrogen and water use simultaneously may be facilitated by understanding the mechanisms that underpin the C4 syndrome. Existing experimental studies have indicated that the emergence of the C4 syndrome requires co-ordination between several levels of cellular organization, from gene regulation to metabolism, across two co-operating cell systems-mesophyll and bundle sheath cells. Yet, determining the extent to which the structure of the C4 plant metabolic network may constrain gene expression remains unclear, although it will provide an important consideration in engineering C4 photosynthesis in C3 plants. Here, we utilize flux coupling analysis with the second-generation maize metabolic models to investigate the correspondence between metabolic network structure and transcriptomic phenotypes along the maize leaf gradient. The examined scenarios with publically available data from independent experiments indicate that the transcriptomic programs of the two cell types are co-ordinated, quantitatively and qualitatively, due to the presence of coupled metabolic reactions in specific metabolic pathways. Taken together, our study demonstrates that precise quantitative coupling will have to be achieved in order to ensure a successfully engineered transition from C3 to C4 crops.

Avoiding the Enumeration of Infeasible Elementary Flux Modes by Including Transcriptional Regulatory Rules in the Enumeration Process Saves Computational Costs

Despite the significant progress made in recent years, the computation of the complete set of elementary flux modes of large or even genome-scale metabolic networks is still impossible. We introduce a novel approach to speed up the calculation of elementary flux modes by including transcriptional regulatory information into the analysis of metabolic networks. Taking into account gene regulation dramatically reduces the solution space and allows the presented algorithm to constantly eliminate biologically infeasible modes at an early stage of the computation procedure. Thereby, computational costs, such as runtime, memory usage, and disk space, are extremely reduced. Moreover, we show that the application of transcriptional rules identifies non-trivial system-wide effects on metabolism. Using the presented algorithm pushes the size of metabolic networks that can be studied by elementary flux modes to new and much higher limits without the loss of predictive quality. This makes unbiased, system-wide predictions in large scale metabolic networks possible without resorting to any optimization principle.

Reconstruction of a generic metabolic network model of cancer cells

A promising strategy for finding new cancer drugs is to use metabolic network models to investigate the essential reactions or genes in cancer cells. In this study, we present a generic constraint-based model of cancer metabolism, which is able to successfully predict the metabolic phenotypes of cancer cells. This model is reconstructed by collecting the available data on tumor suppressor genes. Notably, we show that the activation of oncogene related reactions can be explained by the inactivation of tumor suppressor genes. We show that in a simulated growth medium similar to the body fluids, our model outperforms the previously proposed model of cancer metabolism in predicting expressed genes.

On correlated reaction sets and coupled reaction sets in metabolic networks

Two reactions are in the same "correlated reaction set" (or "Co-Set") if their fluxes are linearly correlated. On the other hand, two reactions are "coupled" if nonzero flux through one reaction implies nonzero flux through the other reaction. Flux correlation analysis has been previously used in the analysis of enzyme dysregulation and enzymopathy, while flux coupling analysis has been used to predict co-expression of genes and to model network evolution. The goal of this paper is to emphasize, through a few examples, that these two concepts are inherently different. In other words, except for the case of full coupling, which implies perfect correlation between two fluxes (R(2) = 1), there are no constraints on Pearson correlation coefficients (CC) in case of any other type of (un)coupling relations. In other words, Pearson CC can take any value between 0 and 1 in other cases. Furthermore, by analyzing genome-scale metabolic networks, we confirm that there are some examples in real networks of bacteria, yeast and human, which approve that flux coupling and flux correlation cannot be used interchangeably.

Generic flux coupling analysis

Flux coupling analysis (FCA) has become a useful tool for aiding metabolic reconstructions and guiding genetic manipulations. Originally, it was introduced for constraint-based models of metabolic networks that are based on the steady-state assumption. Recently, we have shown that the steady-state assumption can be replaced by a weaker lattice-theoretic property related to the supports of metabolic fluxes. In this paper, we further extend our approach and develop an efficient algorithm for generic flux coupling analysis that works with any kind of qualitative pathway model. We illustrate our method by thermodynamic flux coupling analysis (tFCA), which allows studying steady-state metabolic models with loop-law thermodynamic constraints. These models do not satisfy the lattice-theoretic properties required in our previous work. For a selection of genome-scale metabolic network reconstructions, we discuss both theoretically and practically, how thermodynamic constraints strengthen the coupling results that can be obtained with classical FCA. A prototype implementation of tFCA is available at http://hoverboard.io/L4FC.

Double and multiple knockout simulations for genome-scale metabolic network reconstructions

Background

Constraint-based modeling of genome-scale metabolic network reconstructions has become a widely used approach in computational biology. Flux coupling analysis is a constraint-based method that analyses the impact of single reaction knockouts on other reactions in the network.

Results

We present an extension of flux coupling analysis for double and multiple gene or reaction knockouts, and develop corresponding algorithms for an in silico simulation. To evaluate our method, we perform a full single and double knockout analysis on a selection of genome-scale metabolic network reconstructions and compare the results.

Software

A prototype implementation of double knockout simulation is available at http://hoverboard.io/L4FC.

Computational prediction of essential metabolic genes using constraint-based approaches

In this chapter, we describe the application of constraint-based modeling to predict the impact of gene deletions on a metabolic phenotype. The metabolic reactions taking place inside cells form large networks, which have been reconstructed at a genome-scale for several organisms at increasing levels of detail. By integrating mathematical modeling techniques with biochemical principles, constraint-based approaches enable predictions of metabolite fluxes and growth under specific environmental conditions or for genetically modified microorganisms. Similar to the experimental knockout of a gene, predicting the essentiality of a metabolic gene for a phenotype further allows to generate hypotheses on its biological function and design of genetic engineering strategies for biotechnological applications. Here, we summarize the principles of constraint-based approaches and provide a detailed description of the procedure to predict the essentiality of metabolic genes with respect to a specific metabolic function. We exemplify the approach by predicting the essentiality of reactions in the citric acid cycle for the production of glucose from fatty acids.

FCDECOMP: Decomposition of metabolic networks based on flux coupling relations

A metabolic network model provides a computational framework to study the metabolism of a cell at the system level. Due to their large sizes and complexity, rational decomposition of these networks into subsystems is a strategy to obtain better insight into the metabolic functions. Additionally, decomposing metabolic networks paves the way to use computational methods that will be otherwise very slow when run on the original genome-scale network. In the present study, we propose FCDECOMP decomposition method based on flux coupling relations (FCRs) between pairs of reaction fluxes. This approach utilizes a genetic algorithm (GA) to obtain subsystems that can be analyzed in isolation, i.e. without considering the reactions of the original network in the analysis. Therefore, we propose that our method is useful for discovering biologically meaningful modules in metabolic networks. As a case study, we show that when this method is applied to the metabolic networks of barley seeds and yeast, the modules are in good agreement with the biological compartments of these networks.

DRUM: a new framework for metabolic modeling under non-balanced growth. Application to the carbon metabolism of unicellular microalgae

Metabolic modeling is a powerful tool to understand, predict and optimize bioprocesses, particularly when they imply intracellular molecules of interest. Unfortunately, the use of metabolic models for time varying metabolic fluxes is hampered by the lack of experimental data required to define and calibrate the kinetic reaction rates of the metabolic pathways. For this reason, metabolic models are often used under the balanced growth hypothesis. However, for some processes such as the photoautotrophic metabolism of microalgae, the balanced-growth assumption appears to be unreasonable because of the synchronization of their circadian cycle on the daily light. Yet, understanding microalgae metabolism is necessary to optimize the production yield of bioprocesses based on this microorganism, as for example production of third-generation biofuels. In this paper, we propose DRUM, a new dynamic metabolic modeling framework that handles the non-balanced growth condition and hence accumulation of intracellular metabolites. The first stage of the approach consists in splitting the metabolic network into sub-networks describing reactions which are spatially close, and which are assumed to satisfy balanced growth condition. The left metabolites interconnecting the sub-networks behave dynamically. Then, thanks to Elementary Flux Mode analysis, each sub-network is reduced to macroscopic reactions, for which simple kinetics are assumed. Finally, an Ordinary Differential Equation system is obtained to describe substrate consumption, biomass production, products excretion and accumulation of some internal metabolites. DRUM was applied to the accumulation of lipids and carbohydrates of the microalgae Tisochrysis lutea under day/night cycles. The resulting model describes accurately experimental data obtained in day/night conditions. It efficiently predicts the accumulation and consumption of lipids and carbohydrates.

Finding elementary flux modes in metabolic networks based on flux balance analysis and flux coupling analysis: application to the analysis of Escherichia coli metabolism

Elementary modes (EMs) are steady-state metabolic flux vectors with minimal set of active reactions. Each EM corresponds to a metabolic pathway. Therefore, studying EMs is helpful for analyzing the production of biotechnologically important metabolites. However, memory requirements for computing EMs may hamper their applicability as, in most genome-scale metabolic models, no EM can be computed due to running out of memory. In this study, we present a method for computing randomly sampled EMs. In this approach, a network reduction algorithm is used for EM computation, which is based on flux balance-based methods. We show that this approach can be used to recover the EMs in the medium- and genome-scale metabolic network models, while the EMs are sampled in an unbiased way. The applicability of such results is shown by computing “estimated” control-effective flux values in Escherichia coli metabolic network.

Studying the relationship between robustness against mutations in metabolic networks and lifestyle of organisms

Robustness is the key feature of biological networks that enables living organisms to keep their homeostatic state and to survive against external and internal perturbations. Variations in environmental conditions or nutrients and intracellular changes such as genetic mutations have the potential to change stability and efficiency of an organism. Structural robustness helps biological systems to choose alternative routes of adaptation to varying conditions. In this study, in order to estimate the structural robustness in metabolic networks we presented a novel flux balance-based approach inspired by bond percolation theory. Fourteen in silico metabolic models were studied in this work in order to examine the possible relationship between the lifestyle of organisms and their metabolic robustness. The results of this study confirm that in organisms which are highly adapted to their environment robustness to mutations may decrease compared to other organisms.

Sybil--efficient constraint-based modelling in R

Background

Constraint-based analyses of metabolic networks are widely used to simulate the properties of genome-scale metabolic networks. Publicly available implementations tend to be slow, impeding large scale analyses such as the genome-wide computation of pairwise gene knock-outs, or the automated search for model improvements. Furthermore, available implementations cannot easily be extended or adapted by users.

Results

Here, we present sybil, an open source software library for constraint-based analyses in R; R is a free, platform-independent environment for statistical computing and graphics that is widely used in bioinformatics. Among other functions, sybil currently provides efficient methods for flux-balance analysis (FBA), MOMA, and ROOM that are about ten times faster than previous implementations when calculating the effect of whole-genome single gene deletions in silico on a complete E. coli metabolic model.

Conclusions

Due to the object-oriented architecture of sybil, users can easily build analysis pipelines in R or even implement their own constraint-based algorithms. Based on its highly efficient communication with different mathematical optimisation programs, sybil facilitates the exploration of high-dimensional optimisation problems on small time scales. Sybil and all its dependencies are open source. Sybil and its documentation are available for download from the comprehensive R archive network (CRAN).

Flux modules in metabolic networks

The huge number of elementary flux modes in genome-scale metabolic networks makes analysis based on elementary flux modes intrinsically difficult. However, it has been shown that the elementary flux modes with optimal yield often contain highly redundant information. The set of optimal-yield elementary flux modes can be compressed using modules. Up to now, this compression was only possible by first enumerating the whole set of all optimal-yield elementary flux modes. We present a direct method for computing modules of the thermodynamically constrained optimal flux space of a metabolic network. This method can be used to decompose the set of optimal-yield elementary flux modes in a modular way and to speed up their computation. In addition, it provides a new form of coupling information that is not obtained by classical flux coupling analysis. We illustrate our approach on a set of model organisms.

Mathematical optimization applications in metabolic networks

Genome-scale metabolic models are increasingly becoming available for a variety of microorganisms. This has spurred the development of a wide array of computational tools, and in particular, mathematical optimization approaches, to assist in fundamental metabolic network analyses and redesign efforts. This review highlights a number of optimization-based frameworks developed towards addressing challenges in the analysis and engineering of metabolic networks. In particular, three major types of studies are covered here including exploring model predictions, correction and improvement of models of metabolism, and redesign of metabolic networks for the targeted overproduction of a desired compound. Overall, the methods reviewed in this paper highlight the diversity of queries, breadth of questions and complexity of redesigns that are amenable to mathematical optimization strategies.